BOSTON (CBS/AP) – A new study says the Moderna and Pfizer COVID-19 vaccines do not appear to pose serious risks during pregnancy.

The preliminary results are based on reports from more than 35,000 women in the U.S. who received either one of the shots while pregnant from December 2020 through February 2021.

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Researchers said the most common side effect was pain at the injection site.

The rates of miscarriage, premature births and other complications were comparable to those observed in published reports on pregnant women before the pandemic.

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This is one of the largest reports on COVID-19 vaccination in pregnancy but scientists say more comprehensive research is needed.

The new evidence from researchers at the federal Centers for Disease Control and Prevention was published Wednesday in the New England Journal of Medicine.

Johnson & Johnson’s vaccine wasn’t available at the time of the study and wasn’t included.

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(© Copyright 2021 CBS Broadcasting Inc. All Rights Reserved. Associated Press Medical Writer Lindsey Tanner contributed to this report.)